Trimmed minimax estimator of a covariance matrix

Dipak K. Dey, C. Srinivasan

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


In the problem of estimating the covariance matrix of a multivariate normal population, James and Stein (Proc. Fourth Berkeley Symp. Math. Statist. Prob., 1, 361-380, Univ. of California Press) obtained a minimax estimator under a scale invariant loss. In this paper we propose an orthogonally invariant trimmed estimator by solving certain differential inequality involving the eigenvalues of the sample covariance matrix. The estimator obtained, truncates the extreme eigenvalues first and then shrinks the larger and expands the smaller sample eigenvalues. Adaptive version of the trimmed estimator is also discussed. Finally some numerical studies are performed using Monte Carlo simulation method and it is observed that the trimmed estimate shows a substantial improvement over the minimax estimator.

Original languageEnglish
Pages (from-to)101-108
Number of pages8
JournalAnnals of the Institute of Statistical Mathematics
Issue number1
StatePublished - Dec 1986


  • adaptive estimator
  • Covariance matrix
  • minimax estimator
  • Stein's loss
  • Stein's truncation
  • Wishart distribution

ASJC Scopus subject areas

  • Statistics and Probability


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